NEILE, WILLIAM (1637–1670), mathematician, was the eldest son of Sir Paul Neile and the grandson of Richard Neile [q. v.], archbishop of York, in whose palace at Bishopthorpe he was born on 7 Dec. 1637. Entering Wadham College, Oxford, as a gentleman-commoner in 1652, but not matriculating in the university till 1655, he soon displayed mathematical genius, which was developed by the instructions of Dr. Wilkins and Dr. Seth Ward. In 1657 he became a student at the Middle Temple. In the same year, at the age of nineteen, he gave an exact rectification of the cubical parabola, and communicated his discovery—the first of its kind—to Brouncker, Wren, and others of the Gresham College Society. His demonstration was published in Wallis's ‘De Cycloide,’ 1659, p. 91. Neile was elected a fellow of the Royal Society on 7 Jan. 1663, and a member of the council on 11 April 1666. His theory of motion was communicated to the society on 29 April 1669 (Birch, Hist. of the Royal Society, ii. 361). He prosecuted astronomical observations with instruments erected on the roof of his father's residence, the ‘Hill House,’ at White Waltham in Berkshire, where he died, in his thirty-third year, on 24 Aug. 1670, ‘to the great grief of his father, and resentment of all virtuosi and good men that were acquainted with his admirable parts’ (Wood). A white marble monument in the parish church of White Waltham commemorates him, and an inscribed slab in the floor marks his burial-place. He belonged to the privy council of Charles II. Hearne says of him, ‘He was a virtuous, sober, pious man, and had such a powerful genius to mathematical learning that had he not been cut off in the prime of his years, in all probability he would have equalled, if not excelled, the celebrated men of that profession. Deep melancholy hastened his end, through his love for a maid of honour, to marry whom he could not obtain his father's consent.’ [Foster's Alumni Oxonienses, 1500–1714, s.v. ‘Neale;’ Wood's Athenæ Oxon. (Bliss), iii. 902; Hearne's Itinerary of John Leland, 2nd edit. 1744, p. 144; Rigaud's Correspondence of Scientific Men, ii. 488, 608; Wallis's Letter on Neile's Invention (Phil. Trans. viii. 6146); Phil. Trans. Abridged, ii. 112 (Hutton); Birch's Hist. of the Royal Soc. ii. 460; Hutton's Mathematical Dict. 1815; Marie's Hist. des Sciences, v. 117; Montucla's Hist. des Mathématiques, ii. 353; Poggendorff's Biog. Lit. Handwörterbuch.]